if a smaller wheel on car causes the larger wheel to rotate at what degrees does the larger tire rotate if the smaller has a radius of 5.4 cm and the largest tire radius is 6.2 cm?the smaller tire...

if a smaller wheel on car causes the larger wheel to rotate at what degrees does the larger tire rotate if the smaller has a radius of 5.4 cm and the largest tire radius is 6.2 cm?the smaller tire rotated 91 degrees.

Since radius of smaller wheel is 5.4cm it follows that its circumference is

`2cdot5.4 pi=10.8pi`cm.

Similarly circumference of larger wheel is

`2cdot6.2 pi=12.4 pi`cm.

If a wheel with circumference length `c` rotates by 1° it has traveled `c/360` because full circle has 360°. So since our smaller wheel has rotated 91° it has traveled `(91cdot10.8pi)/360=2.73pi`cm. The larger wheel must travel the same as the smaller one, hence we have